Originally posted by Joshua Feingold:

If not known or the card is not supposed to be on top, reveal the card to both players

“Judge, you just showed him my secret sideboard tech!!!”

Be careful about things like that. If you only reveal it to its owner, there's still a chance that it's the card they would draw next - i.e., it should have been on top of the library - and it may be exactly what they need at that point in the game. And now, you've helped them look at extra cards, so you're going to have to shuffle away the card they think they should be able to topdeck.

Instead, I think the way Ernst handled it - looking but not revealing, then letting that guide his line of questioning - is ideal. It's also a great example of how to shortcut a “countback” (I'll admit, I'd not heard that term before). I think attempting to work back, counting cards, is a fine technique for resolving situations like this, or claims of “he has an extra card!”.

However, as Josh points out, that can be time-consuming; don't become obsessed by solving the card count puzzle. Instead, at some point, realize that it's going to be more complicated than valuable, and proceed as best you can.
(My memory says there was an article about how to count, how to discount card draws, “cantrips”, etc., and do it efficiently; weird web access restrictions means I can't search for, and link to, that article…)

d:^D

Originally posted by Scott Marshall:

(My memory says there was an article about how to count, how to discount card draws, “cantrips”, etc., and do it efficiently; weird web access restrictions means I can't search for, and link to, that article…)

I searched in the Judge Articles Index but found nothing :( If someone knows the link and could post it I would be really thankful because this sounds like an intresting topic.

Originally posted by Joshua Feingold:

If not known or the card is not supposed to be on top, reveal the card to both players. Ask if both players think it should be in the graveyard.

I really, really don't like the idea of any solution which involves revealing potentially hidden information from player A's 75 to player B. That feels like something we should strive to avoid.

I think Ernst's solution worked out well. And, if you can help the players resolve it themselves in a timely fashion, that is the best possible outcome.

I also agree that you should be cautious about revealing potentially hidden information. However, we are in a scenario where there are roughly even odds that the card's identity is already known. And, if it isn't known, the players' metagame knowledge or a previous game has likely already revealed that the card would be in the deck anyway. (For example, if the card is a basic Island, revealing it is basically never giving anything away.)

You should proceed with a bit less bravado that I suggested in my previous post when deciding to reveal a card. You likely want to assess whether you are letting the cat out of the bag in some respect before you reveal anything to anyone. However, Scott got very nicely at what I was really trying to say:

Originally posted by Scott Marshall:

don't become obsessed by solving the card count puzzle. Instead, at some point, realize that it's going to be more complicated than valuable, and proceed as best you can.

Whatever route you decide to go in your investigation, have an exit strategy. And when the problem is something relatively low-impact on the course of the game, be prepared to invoke that exit strategy before you spend too much time.

Originally posted by Scott Marshall:

(My memory says there was an article about how to count, how to discount card draws, “cantrips”, etc., and do it efficiently; weird web access restrictions means I can't search for, and link to, that article…)

My memory is saying that too, but all I can find is this by Riccardo Tessitori:

http://www.blackborder.com/q/node/14910

(scroll down to the cartoon of two people arguing)

In my experience it helps to practice, perhaps by stopping a game with a friend halfway through and see what you can determine.

Originally posted by Martha Lufkin:

My memory is saying that too, but all I can find is this by Riccardo Tessitori:

http://www.blackborder.com/q/node/14910

(scroll down to the cartoon of two people arguing)

In my experience it helps to practice, perhaps by stopping a game with a friend halfway through and see what you can determine.

That's already quite nice. I think it's great to have some basics to not be overwhelmed when it actually happens. Thanks for finding it!

This report from Kevin also talk about how to efficiently count cards: http://blogs.magicjudges.org/whatsupdocs/2014/12/17/from-counting-cards-to-reconstructing-game-states/